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Mathematical models for cellular systems. The von foerster equation. Part II

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Abstract

This is the continuation of Part I, which was published in the September, 1965, issue of theBulletin. The birth rate, α(t), is now assumed to be a linear functional of the age density,n. This gives a simple model of self-replenishing stem cell compartments, and leads to a necessary condition for the existence of a steady state. Some examples are presented to illustrate the formalism. They include: (a) An equivivant population with life spanD and no losses from death or migration. The total number of cells is multiplied by 2 in each time intervalD. As a special case, frequently realized in practice, the population may be increasing exponentially with time (“log-phase” of growth). (b) A compartment with “random” emigration of cells and gamma distribution of life spans. (c) An oversimplified version of L. G. Lajtha’s model describing stem cell kinetics. In section IV a simple case in which the loss function depends explicitly onn is discussed very briefly.

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This work was performed under the auspices of the U.S. Atomic Energy Commission.

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Trucco, E. Mathematical models for cellular systems. The von foerster equation. Part II. Bulletin of Mathematical Biophysics 27, 449–471 (1965). https://doi.org/10.1007/BF02476849

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